First-principles characterization for the nitrogen dimer electronic free energy surface within the free-energy Born—Oppenheimer approximation.

We investigate the free energy surface for the nitrogen dimer within the free-energy Born—Oppenheimer (FEBO) approximation. Our initial investigations calculated the exact internal energy (U), entropy (S), and free energy (F) using finite-temperature full configuration interaction. Considering only the electronic degree of freedom we observed the free energy surface predicts a dissociation at temperatures below the experimental dissociation energy. To explain this behavior, we compared the contributions from U and S to F and found that the two quantities have opposing effects on the free energy, with the entropic contribution promoting dissociation. We also explored how the symmetries used within the Hamiltonian impact the temperature for dissociation and found that more symmetries resulted in lower temperatures for dissociation. To test the impact of basis set size, we used the density matrix quantum Monte Carlo (DMQMC) family of methods to simulate the finite temperature density matrix in a cc-pVDZ basis set. We found that the larger basis set resulted in the temperature for dissociation increasing. Finally, we explored the origins of this behavior using histograms for the density matrix elements. We observed that the histogram for longer bond lengths showed more variation across temperature compared to shorter bonds. Additionally, the longer bond length histograms shared many similarities with ground state histograms for multi-reference systems.